The interband Faraday rotation of semiconductors, i.e. the rotation not specifically due to free carriers, shows an unusual variety of behaviour. Whereas the rotation of ionic crystals and insulators is generally positive at all frequencies below the absorption edge, in InSb and InAs it is unusually large and negative and in Ge and GaSb it is positive at low frequencies but passes through a maximum and becomes negative as the frequency is increased towards the absorption edge. The interband Faraday rotation is analyzed here on the basis of the Luttinger-Kohn model. Effective mass parameters and other band constants previously determined have been employed in computations for GaAs, GaSb, Ge, InAs and InSb. The qualitative features of the observed interband rotations are correctly predicted by this model. This analysis shows that the observed interband rotation is principally determined by a competition between (virtual) transitions from the heavy valence states (a positive term) and the light valence states (a negative term). A small energy gap and small valence effective masses favour the light over the heavy valence band contribution; and conversely for a large gap and large valence masses. Ge lies in the middle of our sequence of five substances and a largely complete cancellation between these two principal contributions leads to an unusually small rotation.